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Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check if they are valid identification numbers?

You are given the method used for assigning certain check codes and
you have to find out if an error in a single digit can be
identified.

Transposition Fix

Age 14 to 16 Challenge Level:

Suppose an operator types a US Bank check code into a machine
and transposes two adjacent digits (i.e. swaps the order of two
adjacent digits) for example the operator types $a_3a_2$ instead of
$a_2a_3$, will the machine pick up every error of this type? Does
the same apply to ISBN numbers; will a machine detect transposition
errors in these numbers?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.